Lingerie dress refers to white, lacy dresses of the period. This one could possibly be made from something sheer which could account for the name. Do you know the source of the image? A dressmaking periodical would provide more details on what fabric to use.

The picture is from the January, 1913 issue of Ladies Home Journal. The magazine sold dress patterns back then. Each month there were images of outfits made using patterns that readers could purchase by mail. I’m not sure, but people may have also been able to purchase the patterns at stores.